Rigid-flexible coupled modeling of compound multistage gear system considering flexibility of shaft and gear elastic deformation

Compound multistage gearing systems are widely used in rotating machinery to provide high speed-reduction ratios and heavy load capacity. Modeling and characterizing the dynamic behavior of compound multistage gear transmission systems provides valuable insights for the design and fault diagnosis of transmission systems. However, modeling compound multistage gear transmission systems still has some challenges due to 1) the complex interactions among multistage gear systems and 2) the flexibility, e.g., gear elastic deformation related to gear time-varying mesh stiffness (TVMS), which is affected by load and has not yet been addressed in analytical method, and shaft flexibility. In this paper, a multistage rigid-flexible model of compound multistage gear transmission systems is proposed to comprehensively understand their dynamic behaviors. The proposed method concerns the flexibility of gears and shafts and further constructs a dynamic analysis model. By this, the load-dependent TVMS considering gear tooth elastic deformation is calculated and compared with the existing method. After that, the ordinary and partial differential equations of gears and shafts are fused to characterize the coupling behaviors among multistage subsystems. Finally, the proposed model is solved using the variables separation method and modal superposition method. The accuracy of the constructed model is verified by experimental response collected from a wind turbine drive train test rig. All the characteristic frequencies and the coupled dynamic response of the whole system are obtained and analyzed. The modal energy distribution of the proposed model is depicted to illustrate the flexibility and load influence on the system operational modal, which provides a theoretical foundation for the design and fault diagnosis of a compound multistage gear system.